[Tristan Lall]

I know you're probably trying to avoid machining it, but if you filled the bearing portion of the threads with a metal-filled epoxy and lathed it down to the correct diameter, you'd do away with the majority of the stress concentration problems, and ensure yourself a precise fit in the bearing. And if you were using mild steel (not hardened) threaded rod, you could even fill it with weld filler, and lathe that down (you'd probably want to clamp it when depositing the weld filler, to avoid distorting the rod, though).

However, I'd tend to agree with the use of a shoulder bolt and a locked nut (threadlocker or a good-quality locknut). McMaster sells several Ø3/8" shoulder bolts in appropriately long sizes, and Flexloc locknuts (which tend to be very secure).